562 PROFESSOR WILLIAM THOMSON’S ACCOUNT OF 
Note.—On the curves described in CLAPEYRON’s graphical method of exhibit- 
ing Carnov’s Theory of the Steam-Engine. 
39. At any instant when the temperature of the water and vapour is ¢, dur- 
ing the fourth operation (see above, § 16), the latent heat of the vapour must be 
precisely equal to the amount of heat that would be necessary to raise the tem- 
perature of the whole mass, if in the liquid state, from ¢ to S.* Hence, if 7 de- 
note the volume of the vapour, c the mean capacity for heat of a pound of water 
between the temperatures S and ¢, and W the weight of the entire mass, in pounds, 
we have 
kv=c (S—2) W. 
Again, the circumstances during the second operation are such that the mass of 
liquid and vapour possesses H units of heat more than during the fourth; and 
consequently, at the instant of the second operation, when the temperature is 2, 
the volume v of the vapour will exceed 7 by an amount of which the latent heat 
is H, so that we have 
40. Now, at any instant, the volume between the piston and its primitive 
position is less than the actual volume of vapour by the volume of the water eva- 
porated. Hence, if z and a denote the abscissze of the curve at the instants of 
the second and fourth operations respectively, when the temperature is 7, we have 
L=v—6v, xe =vV—oN, 
and, therefore, by the preceding equations, 
i 
7 {H+¢ (S—4 W} er a) 

vatZte(S—-)W ern aah (Gl 

These equations, along with 
eof py. VG ed... Ree oee) 
enable us to calculate, from the data supplied by ReGnauut, the abscissa and 
ordinate for each of the curves described above (§ 17), corresponding to any as- 
* For, at the end of the fourth operation, the whole mass is liquid, and at the temperature ¢. 
Now, this state might be arrived at by first compressing the vapour into water at the temperature ¢, 
and then raising the temperature of the liquid to 8; and however this state may be arrived at, there 
cannot, on the whole, be any heat added to or subtracted from the contents of the cylinder, since, 
during the fourth operation, there is neither gain nor loss of heat. This reasoning is, of course, 
founded on Carnot’s fundamental principle, which is tacitly assumed in the commonly-received ideas 
connected with ‘“‘ Watt’s law,” the “latent heat of steam,” and “ the total heat of steam.” 



